The production and use of solid fuel rocket motors is based on a well-developed body of theory and experience. One class of relatively small solid fuel rocket motors is used as apogee or perogee motors to increase the kinetic energy of a spacecraft from a relatively low lying orbit to a different, higher orbit. When fired, the spacecraft comprises the ultimate payload (a satellite, for example) plus at least the motor being fired. Typically, these types of solid fuel rocket motors are fired with the spacecraft in a spinning condition, for enhanced stability and thus the motor being fired is also spinning.
Over the last several years, several applications of one particular motor have illustrated a undesirable nutation of the motor during the actual firing, and even afterwards. Such nutation is generally undesirable for a number of reasons, not the least of which is that it tends to render the spacecraft unstable.
Although nutation is a relatively well-understood phenomenon, and techniques for its control are also well known, see for example U.S. Pat. Nos. 3,442,468; 3,728,900; 3,730,457; 3,737,118 and 3,915,416, those skilled in the art were (and to our knowledge still are) unable to identify the causes of this undesirable nutation and hence were unable to suggest corrections therefore. For example, the nutation control devices described in the referenced patents all require auxiliary apparatus to be located either within or without a spacecraft. While the addition of nutation control apparatus to a body which is to be ultimately placed in orbit has been accomplished, application of these solutions to a rocket motor do not appear feasible. Auxiliary apparatus located outside a rocket motor would merely degrade performance; and the environment within the rocket motor is too hostile for such apparatus, i.e. during firing the pressures within the motor are high, and temperatures are measured in thousands of degrees. Furthermore, since the cause of the nutation was unknown, the effect of such auxiliary apparatus was unknown.
The particular rocket motor within which this nutation was noticed included a relatively new feature related to the placement of the nozzle relative to the motor housing or shell, more particularly the nozzle was deeply submerged. Those skilled in the art are well aware that rocket motor performance is directly related to the length of the nozzle and hence relatively long nozzles are desirable. On the other hand, efforts to fit spacecraft within the cross-section of the Space Transportation System (hereinafter STS) require an effort at shortening the longitudinal extent of the spacecraft. Lengthening of the nozzle would require decreasing the length or longitudinal extent of the spacecraft or require a reduction in longitudinal extent of some other portion of the spacecraft. This problem was solved by lengthening the nozzle, but submerging it within the housing or shell of the rocket motor such that the extent of the nozzle exterior of the rocket motor was relatively short.
Through an analysis of telemetry data, we have come to the conclusion that the nutation exhibited by this rocket motor (particularly the STAR-48) is directly related to the deeply submerged nozzle, and is caused by trapping of combustion products, hereinafter termed slag, within the motor housing, but outboard of the deeply submerged nozzle. The data which leads us to this conclusion is primarily the sharp increase in nutation which is indicated just prior to termination of the motor burn. We believe this is indicative of the presence of slag for the following reason. During the motor burn, any mass within the motor is subject to two forces, a centrifugal force caused by reason of the spinning, and an acceleration force as a result of the rocket burn (i.e., the rocket thrust). During burn, the rocket thrust is very much greater than the centrifugal forces and causes the slag to remain in the annular region around the submerged nozzle at the base of the motor case. Furthermore, when there is no nutation and the body spins smoothly around the spin axis, the mass of the slag would be uniformly distributed around the annular ring due to the centrifugal force and the center of mass of the slag would lie on the spin axis. However, in the presence of nutation or in the presence of dynamic unbalance of the rest of the body, the centrifugal forces are modulated causing the mass of slag to be nonuniformly distributed about the spin axis, which in turn causes the center of mass of the slag to be offset to one side of the spin axis. When the center of mass of the slag is offset from the spin axis, which is the line of action of the thrust, a torque about the center of mass of the entire body is created in a direction perpendicular to the spin axis. This torque changes the nutation, either decreasing or increasing the nutation depending on the parameters of the system, primarily spin rate, inertia ratio, thrust, location of the center of mass, mass of the slag and body, and the geometry of the case. After termination of the rocket burn, the acceleration force is no longer present and the centrifugal force due to the motor spinning tends to push the slag radially outward from the axis of rotation and thus increase the moment of inertia of the slag. This is consistent with a decrease in nutation during burn, followed by a sharp increase in the nutation angle just prior to burn termination, followed by a very much smaller increase in nutation after termination of burn. The deeply submerged nozzle has a tendency to trap products of combustion which is not true of other nozzles. Once trapped, the slag cannot escape and its presence, and especially its movement in response to external forces, produces the undesirable nutation build-up.